Semidefinite optimization (REF ) and (REF ) is a powerful computational tool in control theory [1]}, combinatorial problems [2]}, non-convex polynomial optimization [3]}, and many other areas [4]}. While interior-point methods can solve SDPs in polynomial time to an arbitrary accuracy in theory [4]}, they are not scalable to address many large-scale problems of practical interest [6]}, [7]}. One main difficulty is due to the need of storage, compute, and factorization an large matrix at each iteration of interior-point methods. Existing general-purpose SDP solvers (including the state-of-the-art solver MOSEK [8]}) are limited to medium-scale problem instances (with \(n\)  less than 1000 and \(m\)  being a few hundreds in ()).
